


Hermione Granger’s Family Tree

by Cat_K



Category: Harry Potter - J. K. Rowling
Genre: Arithmancy, Canon Compliant, Dumbledore–Grindelwald duel (mentioned), Dysfunctional teacher, Gen, Hermione Granger – black or white, Hermione Granger’s ethnicity, Hermione Granger’s family tree, Hogwarts Sixth Year, Homework, Magical Theory, Potions, St Mungo's (mentioned), The Golden Trio, potions homework
Language: English
Status: Completed
Published: 2018-11-05
Updated: 2018-11-05
Packaged: 2019-08-19 07:34:11
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 2,957
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/16530218
Author URL: https://archiveofourown.org/users/Cat_K/pseuds/Cat_K
Summary: For a homework assignment at NEWT level, Hermione has to describe her family tree and her ethnic background as precisely as possible.





	Hermione Granger’s Family Tree

**Author's Note:**

> Part 2.2 of Hermione’s homework contains a lot of math. Skip that part if you’re allergic ...  
> And if you don’t like the font (patterned after the books) or Snape’s red, click on the “Hide Creator's Style” button at the top of the page.

Hermione Granger  
October 7th, 1996  
Homework assignment  
Subject: Potions  
Teacher: Professor Snape  
Topic: The Family Background as part of the Personal Background.  
Assignment: 1) Theory: Give a short overview over the concept of the Personal Background (maximum length 1 foot); 2) Praxis: Compile your personal Family Background. First give a precise description of your ancestors’ Geographical Backgrounds, then calculate your Family Background using this data. Explain each step. Minimal depth: grandparents, maximal depth: great-great-great-grandparents. Round percentages to 3rd decimal.  
Date due: October 12th, 1996.

1\. Theoretical Part: Overview over the Concept of the Personal Background

Any magic done by or on any witch or wizard according to official standard procedure may lead to good to very good results. However, knowing the material, spiritual and magical backgrounds both of the magical agent (i.e. the witch or wizard performing the magic) and/or the magical recipient (i.e. the witch or wizard the magic is aimed at) will improve the results and may in fact, depending on the abilities of the witch or wizard performing the magic, lead to vastly superior results. This holds true for all branches of magic, be it potions, charms, transfiguration, or any other.

A good example of this phenomenon can be found in the healing arts. Any potion brewed to exacting standard by a qualified healer or a qualified potioneer will lead to standard grade O results. However, if the brewer takes their personal background into account and accordingly tweaks the brewing process, the resulting potion will be much stronger and be graded O+, subgraded further according to the Kneale-Knox Scale of Potion Perfection. Such potions are much more effective and come with less side effects, and the healing process will be much faster. For this reason, for example, all trainee healers at St Mungo’s are required to research and classify their personal backgrounds to a high precision as an important part of their training programme (much more precisely than can be done within the scope of this homework). All external potioneers supplying St. Mungo’s with ready-brewed potions are required to do the same. The potions can be further refined according to the backgrounds of the patients they are used on. With made-to-order potions the patient’s background will influence both the brewing process and the usage of the potions, with ready-made potions at least the usage will be influenced. For this reason personal backgrounds are compiled for all incoming patients at St Mungo’s, though in most cases obviously to a much less detailed degree than those for the healers and potioneers.

Further examples concerning cases where both agent and recipient are witches or wizards are offensive and defensive spells in witching duels, for which reason usually a lot of preparation in advance of a pre-planned duel goes into researching the background of the opponent. A famous case of this is Albus Dumbledore’s exhaustive research into Gellert Grindelwald in preparation for taking him on in a one-on-one duel to end Grindelwald’s reign of terror.

In cases where the recipient of a spell is an inanimate object the repercussions of the agent factoring in their personal background or not will mostly be much less serious, but the differences will be felt in any spell, up to and including basic house-holding spells. The same goes for recipient-less, intransitive spells like apparating or flooing. The risk of ending up on one’s behind is much lower to non-existent for those who truly know what they are doing as opposed to those who simply and unthinkingly go through the standard procedure.

A multitude of factors may influence one’s background and thus have to be researched for a thorough compilation of a personal background. These include bodily traits like build (size, breadth, proportions, etc., i.e. tall or small, slender or stocky, etc.), mass (weight to height ratio), body tone, etc.; physiologic and neurologic traits (thinker vs. doer, visual, auditory or tactile type, etc.); and magical traits (wand preferences, choice of Hogwarts house, subject preferences, i.e. preferences for potions, charms, transfiguration or divination, etc.) Each of these range of traits may be researched only roughly or to an infinitesimal degree – anybody buying their first wand at age eleven will remember being measured between the nostrils ...

The basis for any compilation of a personal background, though, is determining the geographical background of the individual in question, firstly their own and secondly that of their ancestors, with parents being the most important and importance decreasing with each generation. The geographical background takes into account the geography and the geology of where a person grew up – in which part of the world, in which part of the country, and in which geological surroundings: on loam, on sand, on lime, on rock, in dry areas or wet, etc. A person who grew up in Australia, no matter their ethnicity, will have a vastly different magical background to one who grew up on the British Isles, and a person who grew up in the chalk downs of Southern England will show marked differences to one who grew up in the marshlands of East Anglia.

For the reasons outlined above, knowing their personal background is of utmost importance for any witch or wizard aspiring to any degree of magical competence, and at Hogwarts, factoring in personal backgrounds is an important part of any magical subject at NEWT level. The first step to be learned by students is calculating the basic geographic background, known in its amalgamated form (individual geographic background plus influence of ancestors’ geographic backgrounds) as “family background”.

2\. Practical Part: My Family Background  
2.1 The Family History

My father’s parents:  
• Grandpa Granger – A Hampshire man, roughly three quarters Anglo-Saxon, one quarter Celt. His ancestors have lived and married in the City of Winchester area for centuries, with the exception of his paternal grandmother, who was Welsh. Family rumour has it that his patrilineal great-grandmother (the mother-in-law of the Welsh grandmother) actually was not a local girl either, but an Australian with an English father and an Aborigine mother. Her husband, my Great-great-great-grandpa Granger, would then have been the first of the so-called “restless” or “voyaging Grangers.” I plan to follow up on this rumour after graduating from Hogwarts, but only once I’ve finished reforming the laws on the so-called “controlling” (i.e. oppressing) of magical creatures.  
• Grandma Granger, née Nǃaniu – a Khoisan (Juǀ'hoan) from north-western Botswana with a degree in English Literature, whom Grandpa Granger had met and fallen in love with while spending a summer vacation with a college friend’s family in Botswana (then still known as Bechuanaland).  
My mother’s parents:  
• Grandpa Siebenhorn – A French colonial, who grew up in French North Africa. His father was an Alsatian from Strasbourg with one colonial Indochinese grandmother, his mother was a Berber with caramel-brown hair and olive-green eyes.  
• Grandma Siebenhorn, née Dikôngô – A Mbenga (Aka) from northern French Congo (today’s Republic of Congo) with a touch of Bantu and a degree in engineering, whom Grandpa Siebenhorn had met and fallen in love with while working in French Equatorial Africa. With the onset of decolonisation, the Siebenhorns moved to France, to the Loire Valley.  
My mother studied dentistry and went to England for, as she thought, one semester. There she met my father. Given their astonishingly similar backgrounds, their sadly similar experiences with racist attitudes, and their shared love for Shakespeare, the two started seeing each other regularly and quickly formed a deep attachment. The rest is history.

(The outward appearance of my Berber great-grandmother may indicate that she had some Vandal ancestry, though possibly the generally lighter appearance of Berbers as opposed to Arabs may have their roots in the Berbers’ history long before the Vandals migrated to Africa from Central Europe. Likewise the fact that both my sub-Saharan indigenous grandmothers were university educated already back in the 1950s may indicate some interesting family history which might have some influence on the family’s magical background. Either of these highly interesting factors cannot be explored within the scope of this homework and has to be left to future research.)

This leads to the following percentages in my ancestry:  
25% Khoisan ⇒ South Africa,  
21.875% Mbenga ⇒ Central Africa,  
18.75% English (or possibly 17.1875% English and 1.5625% Aborigine) ⇒ Hampshire, England (possibly also Australia),  
12.5% Berber ⇒ North Africa,  
6.25% Welsh ⇒ North Wales,  
6.25% German-Alsatian ⇒ Alsace, France,  
3.125% Bantu ⇒ Central Africa,  
3.125% French(-Alsatian) ⇒ French, possibly but not necessarily from Alsace,  
3.125% Indochinese ⇒ Indochina.

For a further refining of this background (exceeding the scope of this homework), the exact geographic locations and their geology will have to be researched.

2.2 Calculating the Influence of the Family History on My Magical Background

As already explained in part 1, a witch’s or wizard’s geographical background is determined by where they grew up, and this geographical background is further influenced by the geographical backgrounds of all ancestors, though the influence decreases with each generation. The sum of a witch’s or wizard’s geographical background together with all ancestral influences is known as a witch’s or wizard’s family background.

The ancestral influence does not decrease linearly, though, but rather by the square of the generation’s Aranyani number. The sequence of Aranyani numbers is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. The first two numbers of the sequence, 0 and 1, are the starting numbers. The third number (the second 1) refers to the individual whose background is being determined, which within the frame of this homework is me, Hermione Granger. The following numbers refer to the following generations, i.e. the 2 to the parents, the 3 to the grandparents, the 5 to the great-grandparents, and so on. For the purpose of this homework, the generations will be calculated up to the great-great-great-grandparents (Aranyani number 13).

The formula for calculating the influence of the geographic background of each generation is   
            x = a% ÷ b²  
with ‘x’ being the influence of an individual from a given generation in percent, ‘a’ the percentage that each individual contributes to their generation (50% for parents, 25% for grandparents, etc.), and ‘b’ the Aranyani number for that generation. For the purpose of this homework, x is rounded to the third decimal.

For parents the formula thus reads:  
            x = 50% ÷ 2² = 50% ÷ 4 = 12.500%  
Ditto for grandparents:  
            x = 25% ÷ 3² = 25% ÷ 9 = 2.778%  
And for great-grandparents:  
            x = 12.5% ÷ 5² = 12.5% ÷ 25 = 0.500%  
For great-great-grandparents:  
            x = 6.25% ÷ 8² = 6.25% ÷ 64 = 0.098%  
For great-great-great-grandparents:  
            x = 3.125% ÷ 13² = 3.125% ÷ 169 = 0.018%

Applying these percentages to my family history as outlined in part 2.1 gives the following results:

{ Here follows a long list with the individual percentages given for each generation }

Adding up the individual results for each geographical area gives the following results for the influence the geographical backgrounds of my ancestors have on me:

16.680 % City of Winchester area, Hampshire, UK  
12.500% Loire Valley, France  
4.314% Botswana (Southern Africa)  
4.314% Republic of Congo (Central Africa)  
2.778% French North Africa (North Africa)  
0.768% Strasbourg, Alsace, France  
0.750% France  
0.134% North Wales, UK  
0.018% Indochina

Altogether, this adds up to 42.256%, which is the percentage of my known family background that is determined by my ancestors. (If further generations were added, the total would approach, but never reach, 42.62%.) To this, my own geographical background has to be added. This can never be more than the sum of the influence of the known geographical backgrounds of my ancestors (Newdigate’s First Law of Magical Interaction of Geographical Backgrounds), i.e. also 42.256% as of now. I turned 17 last month and I spent the first twelve years of my life in the City of Winchester area and the last five at Hogwarts. My own geographical background thus at this point in time would add 29.828% City of Winchester area, UK, and 12.428% Hogwarts, Scotland, UK, to my family background. In all, this leaves 15.488% of my family background undetermined. This part cannot be determined (Newdigate’s Second Law of Magical Interaction of Geographical Backgrounds), and I will have to rely on my magical instincts to allow for these 15.488% in any magical action.

As a last step, I have to figure in that I have not yet reached my magical maturity. The influence of my ancestors’ geographical backgrounds is thus still larger than described above, and own geographical background is smaller. Magical maturity is attained at 24 years of age. As I am now 17, my magical maturity is only 70,833% of what it will come to be. My own geographical background thus at this point in time is 29.166% smaller than the numbers given above, while the influence of my ancestors’ geographical backgrounds is 29.166% larger (Newdigate’s Third Law of Magical Interaction of Geographical Backgrounds).

Thus, at this point in time my family background is: 

42.673% City of Winchester area, Hampshire, UK  
16.146% Loire Valley, France  
8.803% Hogwarts, Scotland, UK  
5.572% Botswana (Southern Africa)  
5.572% Republic of Congo (Central Africa)  
3.588% French North Africa (North Africa)  
0.992% Strasbourg, Alsace, France  
0.969% France  
0.173% North Wales, UK  
0.023% Indochina

15,489% undeterminable

_ Length of the theoretical part was to be 1 foot; yours is closer to 1½ foot, despite your abysmally small handwriting. At the risk of repeating myself: I as a teacher have got better things to do than correcting overlong homework turned in by overzealous students. In future, adhere to the stated length! _

_ Part 1 is correct overall and sufficient. _

_Part 2.1 contains inadequate wording and superfluous material:_  
_— ‘Grandpa’ and ‘grandma’ may be acceptable in colloquial speech. In a student’s essay I expect ‘grandfather’ and ‘grandmother’._  
_— Family rumours, educational degrees, bodily traits, the former names of colonies, etc. are outside the scope of the assignment, even more so who fell in love with whom, and your personal plans for your future are completely irrelevant to the topic._  
_— The list of percentages in your ancestry at the end of this section is superfluous here and in fact unusable for further work, as it does not distinguish between generations. It should have been left out completely._  
_— This written part of your family history is less precise than your quantitative analysis in part 2.2; missing for example is a precise description of your Alsatian ancestry or of your Bantu ancestry. This written part forms the basis of the later quantitative analysis and should contain every pertinent fact! ½ point will be deducted._

_ Part 2.2 is correct overall and sufficient. _

_ 11.5 / 12 points _

_ S. Snape _

— — —

Hermione flopped down in one of the stuffed chairs by the common room fire, seething.

‘All the work I put into this, and all the needed material is in there, and then he goes on about “superfluous material” and deducts a point because some of it isn’t in there twice! Urgh, just who does he think he is!’

‘It’s OK, Hermione, it’s done and over with,’ grumbled Ron, ‘there’s no need to go over it again! And it was only ½ point, just be glad it _wasn’t_ one or even more points! And if all that stuff was superfluous there was no need to put it in there, I mean, please, Hermione, your great-grandmother’s eye colour!’

‘It wasn’t superfluous, I explained that all that might point to further interesting details about my background, he simply ignored that!’ said Hermione, a thunderous expression on her face.

‘Yeah, well maybe you should have simply ignored that stuff, too,’ smirked Ron.

Hermione angrily opened her mouth, but Harry cut in. ‘I overheard Malfoy gloating; he said he’d put in lots of stuff that might be of further interest that he’d freely invented, and he said Snape gave him extra points for it.’

‘Figures,’ replied Ron casually. ‘That’s Snape for you, we’ve known him for five years now, what else would you expect?’

Hermione sighed. ‘I guess I was a bit too relaxed in the wording of the family history ...’

Ron sneered again, but before he could say something to further enrage Hermione, Harry quickly cut him off. ‘That doesn’t sound like you, you know, too relaxed in your wording ...?’

‘It was the family thing,’ said Hermione, embarrassed. ‘I didn’t know all this stuff, just the most basic things, that my mum is from the Loire Valley and that both my grandmothers grew up in Africa. But all these details about Alsace and Wales and Australia, the Indochinese and the Berber ancestors, and where exactly my grandmothers came from, I didn’t know any of this till my parents and grandparents owled me all that information now. It’s so fascinating! So I got a bit carried away when I wrote about that ...’

‘Which, knowing you, will never happen again,’ interrupted Ron. ‘Speaking of which, what’s up next for homework?’

‘Some essay for Charms,’ said Harry and reached for his bag to look, but Hermione was quicker. ‘Also a background topic and not directly subject-related: _“I like a healthy breeze round my privates, thank you” – Explain why tight clothing lowers the fertility of wizards and why it interferes with the magic of both wizards and witches, and describe the magical, biological and cultural aspects of these phenomena._ Due on Monday.’

Ron groaned and covered his face with his hands. ‘NEWT level is a horror! I should have left directly after my OWLs and never returned!’

‘And done what then?’ Hermione asked fondly. ‘Stop grousing, you, we should go to the library and get started now!’

‘Game of chess?’ Ron asked Harry.

‘Game of chess!’ Harry answered.  


**Author's Note:**

>   * This started out by me idly thinking up Hermione family history after only now coming across that ‘Hermione – black or white’ stormlet that blew through the internet some time ago. Then somehow this family history turned into a piece of homework done by Hermione ... 
>   * Holistic curriculum (not expressively canon): The Hogwarts curriculum is not just missing the natural sciences (the muggle counterparts to the witching world’s magical sciences), but also all those ‘neutral’ subjects that are needed for a complete education: mathematics, English, geography, foreign languages, social studies, arts and crafts, music, etc. The most likely explanation is that magical curricula are not atomistic but holistic, that is subjects are not taught independently of each other like in Muggle schools, but crossdisciplinary, within the context of other subjects. Topics like “Personal Background” or “Ill Effects of Too Tight Clothing” might be taught as part of ‘Magical Biology’ if such a subject existed, but in the witching world they are seen as interrelated with the main magical subjects and taught as part of them.
>   * Mrs Granger’s maiden name (non-canon): The maiden name of Hermione’s mother is never mentioned in canon. I came across the name Siebenhorn in the genealogy of a Strasbourg family living at the time of the Thirty Years’ War and chose it as it contains the magical number seven (sieben in German). 
>   * Professional potion grading (non-canon): “Any potion brewed to exacting standard by a qualified healer or a qualified potioneer will lead to standard grade O results” – for the purpose of this text professional potion grading is mostly identical to the [grading used at Hogwarts](https://www.hp-lexicon.org/thing/grades-at-hogwarts/) (O, E, A, P, D, T), with O being the highest grade, followed by E, etc., and T being the lowest grade. 
>   * Aranyani numbers (non-canon): In mathemancy, the Aranyani numbers (also known as the Red Lion numbers) are the numbers in the so-called Aranyani sequence, which is characterized by the fact that every number after the first two is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …  
>    
>  Aranyani was an Indian guardian of wild nature and wild animals in the first millennium BCE. Together with the Indian poet and mathemancer Piṅgala (also known as the Red Lion) – or maybe Piṅgala was an alternate identity of hers, accounts vary – she discovered the sequence of numbers later named after her. Aranyani numbers play an important role in biological nature, and even more so in magical nature. Aranyani and Piṅgala were the first to investigate the properties of this sequence of numbers, many more came after them.  
>    
>  Incidentally, when not counting the zero, the 12th number in the sequence is equal to 12 × 12. Which is an indicator of just how magical Aranyani numbers are.  
>    
>  Even more incidentally, Aranyani numbers are also known in Muggle arithmetics, but by a different name. And obviously Muggles are not aware of the magical properties of this and other numerical sequences.  
>    
>  Further numerical sequences:  
>    
>  In many cases where normally Aranyani numbers are used for magical purposes, dark magic prefers to use the Lucius numbers, named after the medieval Italian wizard Lucius. The sequence of Lucius numbers is: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, …  
>  From time to time, dark wizards and witches even attempt to use Lucius numbers when calculating their family backgrounds. The results of using magic modified according to a personal background calculated with the use of Lucius numbers usually are not good and often gruesome. A well-known example is the infamous case of the Hounslow housewife, a deep-dark witch, whose attempt at chopping carrots went disastrously wrong.  
>    
>  Another magical number sequence is the Pandora sequence, discovered by the ancient Greek witch Pandora: 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, ...  
>  Not much is known about this sequence, but it seems to be incompatible with any form of dark magic. Pandora Lovegood is rumoured to have experimented with Pandora numbers. And Xenophilius Lovegood is said to claim that the Pandora sequence describes the reproduction rate of the common mellifly ( _Mellifluosa melliflua_ ).
> 



End file.
